[tex]\displaystyle\\
\text{Se da: }\\
x^3-3x^2-10x=(x+a)(x+b)(x+c)\\
\text{Se cere" }\\
a, ~b, ~c \in Z\\
\text{Practic se cere descompunerea polinomului }~ x^3-3x^2-10x\\\\
\text{Rezolvam }\\
x^3-3x^2-10x=\\
=x(x^2-3x-10)=\\
~~~~~~~~(-3x = -5x+2x)\\
=x(x^2-5x+2x-10)=\\
=x(x(x-5)+2(x-5))=\\
=\boxed{x(x-5)(x+2)}\\
~~~~~~~~\text{Il scriem sub forma: }~(x+a)(x+b)(x+c)\\\\
x(x-5)(x+2) = \boxed{(x+0)(x+(-5))(x+2)}\\\\
\boxed{\Longrightarrow~~\begin{cases} a=0\\b=-5\\c=2
\end{cases}}[/tex]